Question

what is the reason for statement 5 in this proof?
a. asa
b. sss
c. aas
d. sas

Explanation:

Step1: Recall triangle congruence criteria

We need to check which congruence criterion (ASA - Angle - Side - Angle, AAS - Angle - Angle - Side, SSS - Side - Side - Side, SAS - Side - Angle - Side) can be used to prove \(\triangle ABD\cong\triangle CBD\).
We know \(AB = BC\) (given), \(\angle ABD=\angle CBD\) (from the angle - bisector definition), and \(BD = BD\) (reflexive property).

Step2: Identify the congruence criterion

The congruence criterion is SAS (Side - Angle - Side). We have two sides (\(AB = BC\) and \(BD = BD\)) and the included angle (\(\angle ABD=\angle CBD\)) equal.

Answer:

D. SAS